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Arbitrage Opportunities in Arbitrage-Free Models of Bond Pricing

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Author Info

  • Backus, D.K.
  • Foresi, S.
  • Zin, S.E.

Abstract

Mathematical models of bond pricing are used by both academics and Wall Street practitioners, with practitioners introducing time-dependent parameters to fit arbitrage-free models to selected asset prices. We show, in a simple one-factor setting, that the ability of such models to reproduce a subset of security prices need not extend to state-contingent claims more generally. The popular Black-Derman-Toy model, for example, overprices call options on long bonds relative to those on short bonds when interest rates exhibit mean reversion. We argue, more generally, that the additional parameters of arbitrage-free models should be complemented by close attention to fundamentals, which might include mean reversion, multiple factors, stochastic volatility, and/or non-normal interest rate distributions.

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Bibliographic Info

Paper provided by Columbia - Graduate School of Business in its series Papers with number 95-02.

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Length: 28 pages
Date of creation: 1994
Date of revision:
Handle: RePEc:fth:colubu:95-02

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Postal: U.S.A.; COLUMBIA UNIVERSITY, GRADUATE SCHOOL OF BUSINESS, PAINE WEBBER , New York, NY 10027 U.S.A
Phone: (212) 854-5553
Web page: http://www.columbia.edu/cu/business/
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Keywords: FINANCIAL MARKET; PRICES;

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References

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  1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 5(2), pages 177-188, November.
  2. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  3. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, Elsevier, vol. 3(2), pages 133-155, July.
  4. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, Annual Reviews, vol. 1(1), pages 69-96, November.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  6. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, American Finance Association, vol. 41(5), pages 1011-29, December.
  7. Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 28(02), pages 235-254, June.
  8. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
  9. Cooley, T.F. & LeRoy, S.F., 1991. "Pricing Interest-Sensitive Claims when Interest Rates Have Stationary Components," Papers, Rochester, Business - General 91-02, Rochester, Business - General.
  10. Stambaugh, Robert F., 1988. "The information in forward rates : Implications for models of the term structure," Journal of Financial Economics, Elsevier, Elsevier, vol. 21(1), pages 41-70, May.
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Citations

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Cited by:
  1. Michael W. Brandt & Amir Yaron, 2003. "Time-Consistent No-Arbitrage Models of the Term Structure," NBER Working Papers 9458, National Bureau of Economic Research, Inc.
  2. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2004. "Nonparametric Estimation of Convergence of Interest Rates: Effects on Bond Pricing," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 03/04, School of Economics and Business Administration, University of Navarra.
  3. Dennis Kristensen, 2004. "A semiparametric single-factor model of the term structure," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 24741, London School of Economics and Political Science, LSE Library.
  4. Jonathan Berk & Richard C. Green & Vasant Naik, 1998. "Optimal Investment, Growth Options, and Security Returns," NBER Working Papers 6627, National Bureau of Economic Research, Inc.
  5. Orazio Di Miscia, 2005. "Term structure of interest models: concept and estimation problem in a continuous-time setting," Finance, EconWPA 0504017, EconWPA.
  6. Xibin Zhang & Robert D. Brooks & Maxwell L. King, 2007. "A Bayesian approach to bandwidth selection for multivariate kernel regression with an application to state-price density estimation," Monash Econometrics and Business Statistics Working Papers, Monash University, Department of Econometrics and Business Statistics 11/07, Monash University, Department of Econometrics and Business Statistics.
  7. David Backus & Silverio Foresi & Chris Telmer, 1998. "Discrete-Time Models of Bond Pricing," NBER Working Papers 6736, National Bureau of Economic Research, Inc.
  8. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, Elsevier, vol. 106(1), pages 27-65, January.
  9. Jin-Chuan Duan & Kris Jacobs, 2001. "Short and Long Memory in Equilibrium Interest Rate Dynamics," CIRANO Working Papers, CIRANO 2001s-22, CIRANO.
  10. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, Elsevier, vol. 62(1), pages 39-66, October.
  11. Adam Golinski & Peter Spencer, 2012. "The Meiselman forward interest rate revision regression as an Affine Term Structure Model," Discussion Papers, Department of Economics, University of York 12/27, Department of Economics, University of York.
  12. Eli M. Remolona & Joseph Dziwura & Irene Pedraza, 1995. "The short end of the forward convergence curve and asymmetric cat's tail convergence," Research Paper, Federal Reserve Bank of New York 9523, Federal Reserve Bank of New York.
  13. Orazio Di Miscia, 2005. "Estimation of continuous-time interest rate models: a nonparametric approach," Finance, EconWPA 0504015, EconWPA.
  14. Leo Krippner, 2005. "An Intertemporally-Consistent and Arbitrage-Free Version of the Nelson and Siegel Class of Yield Curve Models," Working Papers in Economics, University of Waikato, Department of Economics 05/01, University of Waikato, Department of Economics.
  15. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.

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